Re: Rotated infinite region
integrate from 1 to infinity the function 1/x to obtain +infinity .this means that surprisingly the area enclosed by the graph 1/x and the x-axis from 1 to infinity is extremely large though it is not seem to be so!. The curve 1/x aproaches the x-axis....it is an asymptote and they meet at a point very far away...infinity.
Rotating the graph of curve y=1/x over the x-axis you have to integrate the function π(1/x)^2 from 1 to infinity but surprisingly you will find the volume to be equal to π
This is the surprise....the curve has an infinite area but if rotated it generates a finite volume...